A mechanically controllable valve-train assembly of the above type is described in DE 10 2004 003 327 A1. This patent application describes an assembly which comprises an eccentric shaft having circumferential control surfaces with eccentric members so as to allow for lift adjustments of gas exchange valves between a zero lift and a maximum lift. This embodiment, apart from offering high variability, is also advantageous in regard to the manufacture and assembly processes. A disadvantage of this embodiment is that the transmission assembly and particularly an intermediate lever of the transmission assembly are supported during their movement on the eccentric shaft, thereby causing a force to act on the eccentric shaft at an off-center position. An average moment of rotation is consequently generated which is not constant along the circumference of the eccentric shaft and which has to be compensated for by the drive means. Dependent on the rotary angle of the eccentric shaft comprising an eccentric member, two positions exist where this moment is zero: the position with the largest lift adjustment and the position with the smallest lift adjustment, while only the position with the smallest lift adjustment will provide a stable equilibrium. This has the consequence, however, that a defect of the drive means will cause the eccentric shaft to be transferred into the position of the stable equilibrium, which, in a construction where the smallest lift adjustment describes a zero lift, will result in a failure of the overall internal combustion machine.